I have matrices that are extremely easy to compute pointwise, but are too large to store. (they are not sparse) On the MATLAB site I was told MATLAB doesnt support computations with non-stored matrices. Is their any other software package out there that does?
If the individual entries of the matrices involved can be calculated on the fly relatively cheaply, as you say, then you could turn to matrix-free methods (also known as black box solvers). Krylov-subspace methods such as GMRES belong to that class of solvers and would be useful for you because they only require that the user calculates matrix-vector products. You can do these matrix-vector products by computing the relevant entries of your matrix on the fly, without storing the whole matrix in memory.
The reverse communication routines in the Fortran version of the code available in Templates for the Solution of Linear Systems would match your requirements.
If the matrices are too large to fit into RAM but reasonably could fit on your hard disk, then you should look at what are called "Out of Core" solvers. These solvers partition the large matrix into blocks that are small enough to be handled one at a time in memory. There are many available codes for both dense and sparse problems, but getting good performance out of an out of core solver often requires tuning the code to the particular I/O performance of the computer that you're using.